Question

Sin²theta + 6 Cos theta - 9 = 0 find the value theta when 0is less than or equal to 360 degree ​

Answer 1

`\sin^2(\theta ) + 6\cos(\theta )-9=0\implies ( ~~ \underline{1-\cos^2(\theta )} ~~ )+ 6\cos(\theta )-9=0 \\\\\\ -\cos^2(\theta )+ 6\cos(\theta )-8=0\hspace{5em}\stackrel{\textit{let's just for a second make}}{\cos(\theta )=Z} \\\\\\ -Z^2+6Z-8=0\implies 0=Z^2-6Z+8\implies 0=(Z-2)(Z-4) \\\\\\ Z= \begin{cases} 2\\ 4 \end{cases}\implies \cos(\theta )= \begin{cases} 2\\ 4 \end{cases}`

now, let's recall that cosine just as sine have a range of -1 and 1 and anything in between, but in this case we have two values, hmmm 2 and 4, those two guys are out of cosine's range, so there are no angles that will meet those cosine values, so we can say, no real solution.